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Matrices and Determinants are important and high-weightage topics that are asked both in the JEE Main and JEE Advanced Exam. The topics carry an approximate weightage of 5-7% and candidates can expect 2 to 3 questions from this section in the exam.
The matrices section focuses on understanding the types of matrices (square, diagonal, or identity matrices), Matrix Operation (addition, subtraction, and multiplication of matrices), Transpose and Inverse of a Matrix.
The most asked topics in the Matrices and Determinants are the Inverse of Matrices, Rank of a Matrix, and System of Equations.
Must Read Articles:
- Download JEE Main Last 10-year PYQ for Free
- Download JEE Main 2025 Shift 1 Question Paper with Detailed Solutions
Below is the list of Matrices and Determinants questions with detailed solutions asked in JEE Main.
Question 1:
Question 2:
Question 3:
Question 4:
Question 5:
Question 6:
Question 7:
Question 8:
Question 9:
Question 10:
JEE Main Mathematics Paper Pattern
The NTA has updated the JEE Main Mathematics Exam Pattern for 2025. Earlier, section B allowed candidates to attempt only 5 out of 10 NVQs, but now all 5 are compulsory.
The detailed exam pattern for JEE Main Mathematics is given below:
| Aspect | Details |
|---|---|
| Mode of Exam | Online Computer-Based Test (CBT) |
| Language of Exam | English, Hindi, Assamese, Bengali, Gujarati, Kannada, Malayalam, Marathi, Odia, Punjabi, Tamil, Telugu, and Urdu |
| Types of Questions | Section A: Multiple Choice Questions (MCQs)Section B: Numerical Value-Based Questions (NVQs) |
| Total Number of Questions |
25 Questions Section A: 20 MCQs Section B: 5 NVQs (All mandatory) |
| Marking Scheme | Correct Answer: +4 marksIncorrect Answer: -1 mark (applies to both MCQs and NVQs)Unanswered/Marked for Review: No marks deducted |
| Total Marks | 100 Marks |
JEE Main Mathematics Chapter-Wise Weightage
Calculus and algebra are the most important sections in the JEE Main Mathematics. These topics carry approximately 35 to 40% weightage in the exam.
The detailed chapter-wise weightage for mathematics is given in the table below for classes 11th and 12th.
Class 11 Mathematics High-weightage Topics:
| Chapter | Approximate Weightage |
|---|---|
| Sets, Relations & Functions | 3.3% |
| Complex Numbers & Quadratic Equations | 3.3% |
| Permutations & Combinations | 3.3% |
| Binomial Theorem | 3.3% |
| Sequences & Series | 6.6% |
| Straight Lines | 6.6% |
| Conic Sections (Parabola, Ellipse, Hyperbola) | 9.9% |
| Trigonometric Equations | 3.3% |
Mathematics Chapter-wise Weightage for Class 12 Topics:
| Chapter | Approximate Weightage |
|---|---|
| Matrices & Determinants | 6.6% |
| Limits, Continuity & Differentiability | 3.3% |
| Integral Calculus (Definite & Indefinite Integrals) | 6.6% |
| Differential Equations | 3.3% |
| Vector Algebra | 3.3% |
| Three-Dimensional Geometry | 6.6% |
| Probability & Statistics | 6.6% |
JEE Main Last 5 Year Mathematics Papers Pdf
You can download the JEE Main last 5 years’ Mathematics pdf with solutions from the table given below:
JEE Main 2024 Mathematics Question Paper Session 1
| Exam Date | Question Paper | Solution PDF |
|---|---|---|
| JEE Main 2024 Feb 1 Shift 2 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 Feb 1 Shift 1 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 Jan 31 Shift 2 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 Jan 31 Shift 1 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 Jan 30 Shift 2 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 Jan 30 Shift 1 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 Jan 29 Shift 2 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 Jan 29 Shift 1 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 Jan 27 Shift 2 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 Jan 27 Shift 1 Mathematics Question Paper | Download | Check Solution |
JEE Main 2024 Mathematics Question Paper Session 2
| Exam Date and Shift | Question Paper | Solution PDF |
|---|---|---|
| JEE Main 2024 April 4 Shift 1 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 April 4 Shift 2 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 April 5 Shift 1 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 April 5 Shift 2 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 April 6 Shift 1 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 April 6 Shift 2 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 April 8 Shift 1 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 April 8 Shift 2 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 April 9 Shift 1 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 April 9 Shift 2 Mathematics Question Paper | Download | Check Solution= |
JEE Main 2023 Mathematics Question Paper
| Exam Date | Mathematics Question Paper PDF |
|---|---|
| Mathematics 6 April Shift 1 Question Paper | Check Here |
| Mathematics 6 April Shift 2 Question Paper | Check Here |
| Mathematics 8 April Shift 1 Question Paper | Check Here |
| Mathematics 8 April Shift 2 Question Paper | Check Here |
| Mathematics 10 April Shift 1 Question Paper | Check Here |
| Mathematics 10 April Shift 2 Question Paper | Check Here |
| Mathematics 11 April Shift 1 Question Paper | Check Here |
| Mathematics 11 April Shift 2 Question Paper | Check Here |
| Mathematics 12 April Shift 1 Question Paper | Check Here |
| Mathematics 13 April Shift 1 Question Paper | Check Here |
| Mathematics 13 April Shift 2 Question Paper | Check Here |
| Mathematics 15 April Shift 1 Question Paper | Check Here |
JEE Main 2023 Mathematics Question Paper Session 1
| Exam Date and Shift | Mathematics Question Paper PDF |
|---|---|
| Mathematics 24 January Shift 1 Question Paper | Check Here |
| Mathematics 24 January Shift 2 Question Paper | Check Here |
| Mathematics 25 January Shift 1 Question Paper | Check Here |
| Mathematics 25 January Shift 2 Question Paper | Check Here |
| Mathematics 29 January Shift 1 Question Paper | Check Here |
| Mathematics 29 January Shift 2 Question Paper | Check Here |
| Mathematics 30 January Shift 1 Question Paper | Check Here |
| Mathematics 30 January Shift 2 Question Paper | Check Here |
| Mathematics 31 January Shift 1 Question Paper | Check Here |
| Mathematics 31 January Shift 2 Question Paper | Check Here |
| Mathematics 1 February Shift 1 Question Paper | Check Here |
| Mathematics 1 February Shift 2 Question Paper | Check Here |
JEE Main 2022 Mathematics Question Paper with Solution PDF
| Exam Date | Shift/ Slot | Question Paper PDF |
|---|---|---|
| July 25 | Shift 1 | Check Here |
| July 25 | Shift 2 | Check Here |
| July 26 | Shift 1 | Check Here |
| July 26 | Shift 2 | Check Here |
| July 27 | Shift 1 | Check Here |
| July 27 | Shift 2 | Check Here |
| July 28 | Shift 1 | Check Here |
| July 28 | Shift 2 | Check Here |
| July 29 | Shift 1 | Check Here |
| July 29 | Shift 2 | Check Here |
JEE Main 2022 Mathematics Question Paper with Solution PDF- Phase 1
| Exam Date | Shift/ Slot | Question Paper PDF |
|---|---|---|
| June 29 | Shift 1 | Check Here |
| June 29 | Shift 2 | Check Here |
| June 28 | Shift 1 | Check Here |
| June 28 | Shift 2 | Check Here |
| June 27 | Shift 1 | Check Here |
| June 27 | Shift 2 | Check Here |
| June 26 | Shift 1 | Check Here |
| June 26 | Shift 2 | Check Here |
| June 25 | Shift 1 | Check Here |
| June 25 | Shift 2 | Check Here |
| June 24 | Shift 1 | Check Here |
| June 24 | Shift 2 | Check Here |
JEE Main 2021 Mathematics Question Paper- Download PDF
JEE Main 2021 Mathematics Question Paper with Solution (Session 4- August)- Download PDF
| Exam Date | Shift/ Slot | Question Paper PDF |
|---|---|---|
| August 26 | Shift 1 | Check Here |
| August 26 | Shift 2 | Check Here |
| August 27 | Shift 1 | Check Here |
| August 27 | Shift 2 | Check Here |
| August 31 | Shift 1 | Check Here |
| August 31 | Shift 2 | Check Here |
| September 1 | Shift 2 | Check Here |
JEE Main 2021 Mathematics Question Paper with Solution (Session3- July)- Download PDF
| Exam Date | Shift/ Slot | JEE Main Question Paper PDF |
|---|---|---|
| July 22 | Shift 2 | Check Here |
| July 25 | Shift 1 | Check Here |
| July 25 | Shift 2 | Check Here |
| July 27 | Shift 1 | Check Here |
| August 3 | Shift 1 | Check Here |
| August 3 | Shift 2 | Check Here |
| August 4 | Shift 1 | Check Here |
| August 4 | Shift 2 | Check Here |
JEE Main 2021 Mathematics Question Paper with Solution (Session 2- March)- Download PDF
| Exam Date | Shift/ Slot | Question Paper PDF |
|---|---|---|
| March 16 | Shift 1 | Check Here |
| March 16 | Shift 2 | Check Here |
| March 17 | Shift 1 | Check Here |
| March 17 | Shift 2 | Check Here |
| March 18 | Shift 1 | Check Here |
| March 18 | Shift 2 | Check Here |
JEE Main 2021 Mathematics Question Paper with Solution (Session 1- February)- Download PDF
| Exam Date | Shift/ Slot | Question Paper PDF |
|---|---|---|
| February 24 | Shift 1 | Check Here |
| February 24 | Shift 2 | Check Here |
| February 25 | Shift 1 | Check Here |
| February 25 | Shift 2 | Check Here |
| February 26 | Shift 1 | Check Here |
| February 26 | Shift 2 | Check Here |
JEE Main 2020 Mathematics Question Paper with Solutions- Download PDF
JEE Main 2020 Mathematics Question Paper with Solutions (Session 2- September)- Download PDF
| Exam Date | Shift/ Slot | Question Paper PDF |
|---|---|---|
| September 2 | Shift 1 | Check Here |
| September 2 | Shift 2 | Check Here |
| September 3 | Shift 1 | Check Here |
| September 3 | Shift 2 | Check Here |
| September 4 | Shift 1 | Check Here |
| September 4 | Shift 2 | Check Here |
| September 5 | Shift 1 | Check Here |
| September 5 | Shift 2 | Check Here |
| September 6 | Shift 1 | Check Here |
| September 6 | Shift 2 | Check Here |
JEE Main 2020 Mathematics Question Paper with Solutions (Session 1- January)- Download PDF
| Exam Date | Shift/ Slot | JEE Main Question Paper PDF |
| January 8 | Shift 1 | Check Here |
| January 8 | Shift 2 | Check Here |
| January 9 | Shift 1 | Check Here |
| January 9 | Shift 2 | Check Here |
Important Books for Mathematics:
Frequently Asked Questions
What is the purpose of determinants and matrices?
The main purpose of matrices and determinants is to simplify the mathematical calculations in solving linear equations. Determinants are used to check the uniqueness of the linear equations, and calculate are/volume in geometry.
While the purpose of matrices representation and manipulation of data and solving equations. These concepts areused in the fields of Physics, Computer graphics, and Engineering.
What is the condition to have a determinant of a matrix?
The determinant of a matrix is only defined for a square matrix. For example: a 2x2 or 3x3 matrix has a determinant, but a non square matrix 2x3 does not have a determinant.
The value of the determinant is zero if the rows and columns of the matrix are linearly dependent, representing that the matrix is singular and non-invertible.
Who is the father of Matrix?
Arthur Cayley is considered the father of Matrix, who developed the matrix theory in mid 19th-Century. Other mathematicians like Leibniz and Cauchy have contributed to the foundational ideas of matrices. But, Arthur Cayley’s work formalized matrix algebra making him the father of Matrices.
Can a determinant be negative?
Yes, a determinant can be positive negative, or zero depending on the value of the matrix. A positive determinant indicates orientation and a negative determinant represents a reflection or inversion. While a zero determinant represents that a matrix is singular, it has no inverse and no solution or infinitely many solutions.
What are the applications of matrices?
Matrices have many applications in various fields Like Physics, Engineering, computer graphics, Cryptography, Statistics, and Data science. It is used as follows:
- In physics and engineering the matrices are used in circuit analysis, mechanics, and quantum physics.
- In computer graphics, matrices are essential for 3D transformations, rotations, and scaling in animation.
- Matrix methods are employed for motion control, trajectory planning, and stability analysis.
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